Cohomology of Presheaves of Monoids

Pilar Carrasco and Antonio M. Cegarra
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Pilar Carrasco: Department Algebra, University of Granada, 18071 Granada, Spain
Antonio M. Cegarra: Department Algebra, University of Granada, 18071 Granada, Spain

Mathematics, 2020, vol. 8, issue 1, 1-35

Abstract: The purpose of this work is to extend Leech cohomology for monoids (and so Eilenberg-Mac Lane cohomology of groups) to presheaves of monoids on an arbitrary small category. The main result states and proves a cohomological classification of monoidal prestacks on a category with values in groupoids with abelian isotropy groups. The paper also includes a cohomological classification for extensions of presheaves of monoids, which is useful to the study of H -extensions of presheaves of regular monoids. The results apply directly in several settings such as presheaves of monoids on a topological space, simplicial monoids, presheaves of simplicial monoids on a topological space, monoids or simplicial monoids on which a fixed monoid or group acts, and so forth.

Keywords: cohomology; presheaf of monoids; monoidal prestack; simplicial set; homotopy colimit (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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